Methods and apparatus for determining optimum exposure threshold for a given photolithographic model

ABSTRACT

A system and method for enhancing process latitude (tolerances) in the fabrication of devices and integrated circuits. A measuring point is selected corresponding to a feature of critical dimension. Then the pattern is convolved with the model, and its value and rate of change are calculated over a range of corresponding values of a first process parameter. Next, an optimum threshold having the largest rate of change, or contrast, is selected. Finally, proximity correction is performed using relevant parameters.

FIELD OF THE INVENTION

The present invention relates generally to a low cost method and systemfor enhancing the tolerances of process steps used to fabricateintegrated circuits and discrete devices, and more specifically to a lowcost method for determining the optimum latitude of the process stepsusing computer modeling.

BACKGROUND OF THE INVENTION

Devices and integrated circuits are fabricated with multiple processingsteps. Integrated circuits are often fabricated with one or moredevices, which may include diodes, capacitors, and different varietiesof transistors. These devices often have microscopic features that canonly be manufactured with critical processing steps that require carefulalignment of equipment used to build the devices.

Critical processing steps are used to fabricate device features havingsmall dimensions, known as critical dimensions. Critical dimensions of adevice often define the performance of the device and its surroundingcircuitry. For example, gate length is a critical dimension of a fieldeffect transistor and establishes, in part, the maximum operatingfrequency of the transistor.

If a critical processing step is not reproducible, the criticaldimension cannot be repeatably obtained. Then, the performance of manydevices and integrated circuits may not be acceptable. As a result,processing yields decrease and production costs increase. It istherefore desirable to enhance the latitude of processing steps,particularly critical processing steps.

A critical dimension can be measured at different stages of device andintegrated circuit fabrication. Fabrication may include many successivesteps. First, energy, such as light, is exposed through a mask onto amasking layer, such as resist. As shown in FIG. 1(a), during exposure(step 110), the critical dimension 101 can be measured as the length ofthe footprint of energy 103 incident on the masking layer 102. Anymasking layer 102 having a minimum dose of energy 103 incident upon itis exposed. Then, the exposed masking layer is developed so that, forexample, only unexposed masking layer 104 remains, as shown in FIG.1(b). During development (step 120), the critical dimension 101 can bemeasured as the distance between unexposed masking layers 104, as shownin FIG. 1(b). Then, as shown in FIG. 1(c), material 105 not covered bythe unexposed masking layer 104 is removed. The removal step (step 130)may be accomplished with etching. The material 105 may be a base layer,such as a semiconductor substrate or wafer. During removal (step 130),the critical dimension 101 can be measured as the distance betweenremaining material 105, as shown in FIG. 1(c). As an alternative toremoval (step 140), a conductor 106 may be deposited between theunexposed masking layer 104 which is then removed, as shown in FIG.1(d). The conductor 106 may form the gate of a transistor. The conductor106 may be metal, doped polysilicon, or a combination thereof. Duringdeposition (step 140), the critical dimension 101 can be measured as thelength of the conductor 106.

Conventionally, enhanced processing latitude for critical dimensions areobtained by modifying the exposure (step 110). The exposure (step 110)is a critical processing step also known as lithography. Optical orphotolithography involves patterning the masking layer 102 with energyfrom light. A photolithographic system 200 is illustrated in FIG. 2.Photolithography entails exposing light 203 through a mask 208 onto themasking layer 102. The masking layer 102 is formed on material 105, suchas a base layer, described above.

The mask 208 is a tool used to construct a device or integrated circuit.The design of the mask is created by a human, a computer or boththereof. The mask 208 has a pattern 209 formed by a mask material 206,such as chrome, adjacent to a translucent material 205, such as quartz.Light 203 passes through the mask 208 where no mask material 206 ispresent. Typically, a lens 207 is placed between the mask 208 and themasking layer 102 to focus the light 203 onto the masking layer 102. Thelight 203 exposes the mask's pattern 209 onto the masking layer 102. Themask material 206 also defines a critical dimension 201 of the mask 208.The critical dimension 201 of the mask 208 corresponds to the criticaldimensions 101, described above, on a wafer. However, the criticaldimension 201 of the mask 208 may not be equivalent to the criticaldimension 101 on the wafer. Often, the amount of mask material 206defining the critical dimension 201 will be modified to enhance thelatitude of the process steps used to fabricate wafer features having acritical dimension 101. Other parameters, such as mask material 206width, exposure dose, and focus, can also be adjusted singly or incombination to achieve the critical dimension 101 on the wafer.

Conventionally, enhanced processing latitude for critical dimensions 101are experimentally obtained by modifying process parameters. A series oftest patterns is created. The test patterns are derived from theoriginal pattern used to create structures having critical dimensions101, but may have mask material edge positions varying about theoriginal pattern defining the critical dimension 101. The test andoriginal patterns are used to fabricate features using a matrix ofprocessing parameters. The processing parameters may includephotolithographic, resist development, and etch effect parameters. Forexample, the photolithographic parameters may include light exposuretime and depth of focus of light. These processing parameters are knownto persons skilled in the art.

Subsequently, one test pattern is chosen that demonstrates the leastsensitivity to variations in process parameters. The chosen test patternmust form a feature with an accurate critical dimension 101 withspecific process parameters. This procedure is laborious and expensivebecause it requires fabricating and analyzing multiple patterns formedwith many different process parameters. Hence, only a finite amount oftest patterns can practically be fabricated with different parameters.As a result of this constraint, process latitude can be enhanced to onlya coarse extent. It is therefore desirable to more accurately andinexpensively enhance the latitude of the process parameters. Thislatitude is sometimes known as the contrast of the process. A highcontrast indicates a high tolerance to process variation. A highcontrast is desirable because a relatively large change in the processwill induce a relatively small change of an edge position, possiblyaffecting a critical dimension 101, on a wafer.

Typically, the mask features are formed with distortion on a device oran integrated circuit as a result of nonlinear process effects.Nonlinear process effects occur during many processing steps, includingexposure (step 110) and development (step 120). For example, distortionmay occur during exposure (step 110) as a result of optical diffraction.Also, distortion may occur during development (step 120) as a result ofresist swelling. Nonlinear processing effects are described in SiliconProcessing for the VLSI Era by Wolf et al., which is herein incorporatedby reference. The nonlinear processing effects can be analyticallydescribed with theoretical or empirical models. These models are knownby persons skilled in the art. For example, optical nonlinear effectsare described in Principles of Optics by Born et al., which is hereinincorporated by reference. Such models may be used to simulatefabrication of a device or an integrated circuit in software, such asthe FAIM program by Vector Technology (Brookline, Mass.), or programsfrom Precim Company (Portland, Oreg.).

Models may consist of one or more kernels, typically three-dimensionalfunctions. When a model is convolved with a pattern, the behavior ofthat pattern at a specific point may be predicted. If many points aretaken, a three-dimensional behavior can be predicted. A model thresholdis a value that, when subtracted from the value of the model, canconvert the modeled behavior to a binary behavior. For example, when athreshold of 0.3 is chosen, the model is convolved with the pattern anda value of 0.35 is returned. Subtracting 0.30 from 0.35 suggests thatthe pattern has a positive behavior at this point. Additionally, ashifted behavior can be used by retaining the calculated differentialmagnitude, e.g., 0.05. This information can be interpreted in any numberof ways, depending on the specific application.

Conventionally, after process latitudes have been coarsely enhanced byexperimentally choosing a test pattern and process parameters, thedefinition of features on the mask may be modified by proximity effectcorrection (PEC). Generally, PEC can be accomplished either manuallyusing experimental data or using simulation software for feedback, orautomatically with software using a rules-based method, or a model-basedmethod. Examples of such software are Optimask from Vector Technology(Brookline, Mass.), Proteus from Precim Company (Portland, Oreg.), andOPRX from Trans Vector Technology (Camarillo, Calif.). Using amodel-based method, the kernels are convolved with the original masklayout, compared to a threshold to determine the distortion, and a newmask pattern is created whose features will have diminished distortionwhen formed in an integrated circuit or device. The use of model-basedPEC is well known to persons skilled in the art. The use of models todiminish distortions in fabricated features is further described in“Fast Sparse Aerial Image Calculation for OPC,” 15th Annual Symposium onPhotomask Technology and Management, 1995, by N. Cobb et al., and“Spatial Filter Models to Describe IC Lithographic Behavior,” theOptical Microlithography SPIE 1997 Proceedings, Vol. 3051, pp. 469-478,by J. P. Stirniman et al., which are hereby incorporated by reference.

The specific process parameters determined by experiment, describedpreviously, can be supplied to proximity effect correction software. Toreduce cost and enhance accuracy, it is desirable to automaticallytransfer the process parameters to the proximity effect correctionsoftware.

SUMMARY OF THE INVENTION

The present invention is a system and method for enhancing processlatitude, or tolerance, in the fabrication of devices and integratedcircuits. A measuring point is selected corresponding to a feature ofcritical dimension. Then the pattern is convolved with the model, andits value and rate of change are calculated over a range ofcorresponding values of a first process parameter. Next, an optimumthreshold having the largest rate of change, or contrast, is selected.Finally, proximity correction is performed using relevant parameters.

The method may be implemented in a computer including a processor and amemory. A first calculating process enables the processor to calculatemodeled behavior values and their rates of change over a range ofcorresponding values of the first process parameter. A secondcalculating process enables the processor to select the optimumthreshold. Proximity correction is performed using the optimumthreshold. Proximity correction can be performed manually usingsimulation software for feedback, or automatically with software.Because the method is implemented in a computer, the model parameterscan be determined efficiently over finer incremental values of the firstprocess parameter. Therefore, the parameters can be more precisely andinexpensively determined.

In one embodiment, the first process parameter may be mask material edgeposition in a computer representation of a mask. In one such embodiment,for instance, the optimum threshold is provided to a proximity effectcorrection process in which the computer representation of the mask ismodified to compensate for proximity effects. As a result, the masks canbe automatically or semi-automatically sequentially optimized forprocess latitude and proximity effect correction with a single computerprogram.

In a second embodiment, the first process parameter may be an opticalparameter of a stepper, for example, numerical aperture. In thisembodiment, the numerical aperture of the model is varied to determinethe value that corresponds to the maximum rate of change of the modeledbehavior. The maximum rate of change of the modeled behavior and itscorresponding optimum threshold are provided to a proximity effectcorrection process in which the computer representation of the mask ismodified to compensate for proximity effects.

Further features and advantages of the present invention, as well as thestructure and operation of the various embodiments of the presentinvention, are described in detail below with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described with reference to the accompanyingdrawings. In the drawings, like reference numbers indicate identical orfunctionally similar elements. Additionally, the leftmost digit(s) of areference number identifies the drawing in which the reference numberfirst appears.

FIG. 1(a) is a cross-sectional view of prior art resist exposure;

FIG. 1(b) is a cross-sectional view of prior art resist development;

FIG. 1(c) is a cross-sectional view of prior art material removal;

FIG. 1(d) is a cross-sectional view of prior art conductor deposition;

FIG. 2 is a cross-sectional view of a prior art photolithography system;

FIG. 3(a) is an aerial view of a computer representation of a mask;

FIG. 3(b) is an aerial view of a computer representation of a wafer;

FIG. 4(a) is a flow chart of a method for modeling a semiconductorprocess;

FIG. 4(b) is a flow chart of method for determining values and rates ofchange of a threshold;

FIG. 4(c) is a flow chart of a method for modeling a photolithographicprocess;

FIG. 5(a) is an illustration of a computer representation of a mask;

FIG. 5(b) is a diagram relating the values and slope of threshold withmask material edge position; and

FIG. 6 is a block diagram of one embodiment of a computer system.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following detailed description of the preferred embodiments,reference is made to the accompanying drawings which form a part hereof,and in which is shown by way of illustration of specific preferredembodiments in which the inventions may be practiced. These embodimentsare described in sufficient detail to enable persons skilled in the artto practice the invention, and it is to be understood that otherembodiments may be utilized and that logical, mechanical and electricalchanges may be made without departing from the spirit and scope of thepresent inventions. The following detailed description is, therefore,not to be taken in a limiting sense, and the scope of the presentinventions is defined only by the appended claims.

There are a large number of combinations of modeled behavior values andmask material edge position, or other process variables, that canprovide a desired wafer edge position in a certain situation. Not all ofthese combinations have desirable process parameters or behaviors. Thepresent invention is a system and method of selecting the best modeledbehavior value, or threshold, based upon the contrast or slope of themodel behavior. Given this threshold, a proximity effect correctionprogram will yield the previously determined mask material edgeposition. When a mask 208 is created from the corrected data, and awafer processed, the process latitude, or contrast of the evaluatedpoint(s) should be maximized. This technique can be extended, andinstead of moving the mask material edge, the modeled behavior valueitself can be varied while keeping the mask material edge constant tofind the best model conditions, such as stepper numerical aperture,focus, or on or off axis settings. Thus, for example, the best steppercondition and threshold can be presented to the proximity effectcorrection software to adjust the mask material edge everywhere on themask 208 accordingly. In one embodiment, this last step is notnecessary, as the best stepper conditions provide the desired result.

In a general sense, what is described below is a computer-implementedmethod for determining an optimal process parameter for the fabricationof devices and integrated circuits comprising selecting an initialposition corresponding to a feature of critical dimension. Then, modeledbehavior values and their rates of change are calculated over a range ofcorresponding values of a first process parameter. Next, an optimumthreshold corresponding to the largest rate of change of the modeledbehavior is selected. Finally, proximity correction is performed usingthe optimal threshold and, possibly, additional information. The presentinvention may arrive at an optimal threshold and, optionally,corresponding process parameters by simulating one or more processingsteps described above. For example, the present invention may simulateonly the exposure step (step 110). Alternatively, the present inventionmay simulate the exposure, development and etch steps (steps 110, 120,130).

The present invention will now be described in detail. In oneembodiment, the first process parameter is the position of a maskmaterial edge in a mask. In such an embodiment, the optimal threshold isdetermined as follows. First, an initial position of a mask materialedge 302 on a computer representation of a mask 304 is selected (step410), as illustrated in FIGS. 3(a) and 4(a). The initial position, inpart, defines a feature of critical dimension on the wafer (e.g., thewidth of a line). FIG. 3(a) illustrates an exemplary initial position306 on a computer representation of a mask 304. A measuring point 308 onthe computer representation of the wafer 312 is then selected and athreshold selected to create an edge 310 at that measuring point 308, asshown in FIG. 3(b). The measuring point 308 on the computerrepresentation of the wafer 312 is located on an edge 310 that defines afeature of critical dimension of a device of the wafer.

Then, the value and rate of change of a modeled behavior at themeasuring point 308 on the computer representation of a wafer 312 over arange of a first process parameters is determined by computer simulation(step 420). Each model value is a potential threshold. In thisembodiment, the modeled behavior value and its rate of change aredependent variables. The measuring point 308 and the first processparameter are independent variables. Thus, for a given measuring point308, the first process parameter is incremented or decremented by adesired amount over a desired range of values. The value and the rate ofchange of the modeled behavior are then calculated at the measuringpoint 308 on the computer representation of the wafer for eachincremental value of the first process parameter. The incremental valuesof the first process parameter, and the corresponding values of themodel and its rate of change may be stored in a table.

In a photolithographic process, for example, the first process parametermay be the edge position 302 of the mask material 206 in the computerrepresentation of the mask 208. This example will be described below inmore detail.

Next, the optimum threshold is selected (step 430). The optimumthreshold is equal to the model value having the greatest rate of changeover the evaluated range of first process parameter values. The optimumthreshold is the point at which processing latitudes are optimized.Thus, both the threshold and the first process parameter can be moreprecisely and inexpensively determined to maximize process latitude.

Then, the optimum threshold and, optionally, the corresponding firstprocess parameter, are provided to a proximity effect correction (PEC)process (step 440). The PEC process modifies the mask material edgepositions 302 over the mask 208 or base layer to compensate forproximity effects (step 450), described above. Thus, the mask or baselayer can be automatically or semi-automatically sequentially optimizedfor process latitude and proximity effect correction with a singlecomputer program.

The value and rate of change of the modeled behavior with respect to themeasuring point 308 on the computer representation of the wafer 312 isdetermined (step 420) in a manner known to persons skilled in the art.Points on either side of measuring point 308 are selected and the rateof change of the modeled behavior across the three points is calculated.In an exemplary embodiment, the value and rate of change of the modeledbehavior may be determined in the manner illustrated in FIG. 4(b).However, other embodiments of methods for determining the value and rateof change, different from the one described below, may also be used.First, the value of the first process parameter is decremented from aninitial value by a first value (step 460). Then, the value of themodeled behavior at the measuring point on the computer representationof the wafer 312 with respect to the first process parameter isdetermined or calculated (step 465) with the models described above.Next, the value of the modeled behavior is determined on the computerrepresentation of the wafer 312 at a location that is offset by a secondvalue from the measuring point 308 in one direction of change of thefirst process parameter (step 470). Then, the modeled behavior value isdetermined on the computer representation of the wafer 312 at a locationthat is offset by the second value from the measuring point 308 in theother direction of change of the first process parameter (step 475).Finally, the rate of change of the modeled behavior, at the measuringpoint 308 and corresponding to the value of the first process parameter,is determined or calculated (step 480). The rate of change is solved(step 480) by first calculating the difference of the modeled behaviorvalues ascertained in steps 470 and 475. Then, the rate of change isdetermined by dividing the difference of the modeled behavior values bytwice the second value. The values and rates of change of the modeledbehavior and the corresponding values of the first parameter are enteredinto the table.

Next, it is determined whether the value and rate of change of themodeled behavior has been calculated for a first process parameter valueequal to the first value (step 485). If these calculations have beenperformed, then the process is stopped (step 490). If these calculationshave not been performed, then the first process parameter value isincremented by a third value (step 487). The third value may be chosenso that the first value can be divided by the third value without aremainder. In one such embodiment, the third value is 2^(−N) times thefirst value, where N is an integer greater than one. After performingstep 487, steps 465, 470, 475, 480, and 485 are repeated.

It should be noted that the change in the first process parameters doesnot have to be symmetric around the initial value of the first processparameter. In addition, the step by which the first process parameter ischanged in determining the optimum threshold does not have to beconstant.

Operation of this exemplary embodiment of the present invention will nowbe described, as shown in FIG. 4(c). However, other embodiments may beperformed differently. First, an initial position 306 on an edge of maskmaterial 206 of the computer representation of the mask 304 which formsa feature of critical dimension is selected (step 492). Next, the valueand rate of change of the modeled behavior are determined about ameasuring point 308 on a computer representation of the wafer 312 over arange of modeled mask material edge positions (step 494). The rate ofchange (step 494) can be calculated by any standard method or can becalculated using the method (steps 470, 475, 480) described above. Inone embodiment of such an approach, the second value ranges between oneand ten nanometers. For instance, the modeled behavior value at themeasuring point and at points ±10 nm from the measuring point may beused to calculate the rate of change in the modeled behavior valueneeded to place an edge 310 at the measuring point 308. The third valuemay be, for example, ten nanometers. Using the iterative technique (step420) described above, the optimum threshold is then determined (step496). Subsequently, the optimum threshold is provided to the PEC processdescribed above (step 497). The PEC process can then correct proximityeffects while maintaining maximum processing latitude. The PEC processmodifies the mask material edge positions 302 to compensate forproximity effects (step 498). Finally, the mask 208 can be fabricated,incorporating the modified modeled mask material edge positions 302,using techniques known by persons skilled in the art (step 499).

Modifying the mask material edge position on the mask 208 to yield themaximum slope of the modeled behavior value at the measuring point 308on the wafer will result in maximized process latitude. Both the modeledbehavior value and the rate of change of the modeled behavior value canbe determined more efficiently over finer variations of mask materialwith this method than by experimentation.

Exemplary results of performing the method described above will now bediscussed. In this example, an optical model process is used. FIG. 5Billustrates a plot of threshold 502 and the rate of change, or slope, ofthe modeled behavior value 504 with respect to change in the modeledmask material edge position 510. The data for this plot was calculatedfor a measuring point 308 on a computer representation of a mask 304,having mask material 206 defining a feature of critical dimension, andcorresponds to steps 492 and 494. In one example, the mask material 206width 503 and length 501 may be respectively 400 nm and 3000 nm, asillustrated in FIG. 5A. The data is extracted from the previouslydescribed table. Modifying the mask material edge position of a mask 208by the amount 510 to yield a maximum slope 508 of the threshold 502 willresult in the latitude of the exposure (step 110) being maximized.Practically, this means that the exposure (step 110) will have enhancedcontrast. Therefore, variations of photolithographic parametersaffecting light intensity, such as exposure time and depth of focus,will have a diminished effect on the fabricated feature dimension ofcritical dimension. The optimum threshold value 506, or modeled behaviorvalue having the maximum slope, is then determined (step 496). Thenoptimum threshold value 506 is provided to the PEC process (step 497) tomodify the mask 208 to compensate for nonlinear effects during theexposure (step 110) that distort the features formed on the maskinglayer 102.

The optimum threshold value 506 can be determined for numerous measuringpoints 308 on the computer representation of the wafer 312. If theoptimum thresh old values 506 vary at the different measuring points308, a statistical analysis can be performed on the optimum thresholdvalues 506. Various forms of statistical analysis are known to personsskilled in the art. Thus, a threshold value that is a function, such asthe mean or median, of the optimum threshold values 506 can bedetermined and conveyed to the PEC process.

In addition, multiple models can be considered in the same way. Multiplemodels may include, for example, models for out-of-focus conditions, ordifferent illumination conditions.

The aforementioned methods may be implemented in a computer system. FIG.6 illustrates an exemplary computer system 605 that includes a centralprocessing unit 610 and memory 620. The memory 620 can be random accessmemory, disk storage, CD-ROM storage, or another type of memory. Withinthe memory 620, the computer system 610 has access to its operatingsystem 630 and user software 640. To implement the method of the presentinvention, user software 640 can include the PROTEUS program along withuser-modified scripts. Alternatively, the user software can beuser-developed software, or software from another vendor.

Conclusion

The present invention is an apparatus and method of determining theoptimum process point in device and integrated circuit fabrication. Thepresent invention uses a computer to increase the accuracy and reducethe cost of determining the best process point. Although specificembodiments have been illustrated and described herein, it will beappreciated by those of ordinary skill in the art that any arrangementwhich is calculated to achieve the same purpose may be substituted forthe specific embodiments shown. This patent is intended to cover anyadaptations or variations of the present invention. For example, thefirst process parameter may represent the focus, numerical aperture,exposure time, or on or off axis settings of a stepper. Also, thepresent invention can be implemented with a variety of masks, including,but not limited to, attenuated phase shift masks, alternating aperturephase shift masks, and chromeless phase shift masks. Also, otherlithography techniques may be used, including, but not limited to,X-ray, ion, and electron beam lithography. Therefore, it is manifestlyintended that this invention be limited only by the claims and theequivalents thereof.

We claim:
 1. A method, in a computer, for determining an optimum processpoint for fabricating a device feature of a critical dimension,comprising: selecting a measuring point on a computer representation ofa wafer corresponding to the feature of the critical dimension;calculating modeled behavior values and their rates of change over arange of corresponding values of a first process parameterrepresentative of mask material edge position; selecting an optimumthreshold value having the largest rate of change around said measuringpoint; and determining the first process parameter value correspondingto the optimum threshold value.
 2. The method of claim 1, whereincalculating modeled behavior values comprises calculating the modeledbehavior values and their rates of change over a range of correspondingvalues of the first process parameter representative of focus.
 3. Themethod of claim 1, wherein calculating modeled behavior values comprisescalculating the modeled behavior values and their rates of change over arange of corresponding values of the first process parameterrepresentative of numerical aperture.
 4. The method of claim 1, whereincalculating modeled behavior values comprises: selecting a point on oneside of the measuring point; calculating a value of the modeled behaviorat each of the points; and calculating a slope through each of thepoints, wherein the slope is a function of the values of the modeledbehavior at each point.
 5. The method of claim 4, wherein calculatingmodeled behavior values further comprises selecting a second point. 6.The method of claim 1, wherein calculating threshold values and theirrates of change comprises: decrementing the value of the first processparameter; calculating the value of the modeled behavior at themeasuring point; determining the value of the modeled behavior at alocation offset from the measuring point in a first direction by asecond value; determining the value of the modeled behavior at alocation offset from the measuring point in a second direction, oppositeto the first direction, by the second value; and calculating the rate ofchange of the modeled behavior corresponding to the first processparameter value.
 7. The method of claim 6, wherein calculating the rateof change comprises: calculating a difference of the modeled behaviorvalues ascertained during determining the values of the modeledbehavior; and dividing the difference of the modeled behavior values bytwice the second value.
 8. A method, in a computer, for determining anoptimum process point for fabricating a device feature of a criticaldimension, comprising: selecting a measuring point on a computerrepresentation of a wafer corresponding to the feature of the criticaldimension; calculating modeled behavior values and their rates of changeover a range of corresponding values of a first process parameterrepresentative of mask material edge position; selecting an optimumthreshold value having the largest rate of change around said measuringpoint; determining the first process parameter value corresponding tothe optimum threshold value; and providing the optimum threshold valueto a proximity effect correction process which modifies the mask patternto compensate for proximity effects.
 9. The method of claim 8, whereincalculating modeled behavior values comprises calculating the modeledbehavior values and their rates of change over a range of correspondingvalues of the first process parameter of a computer representation of amask.
 10. The method of claim 8, wherein calculating modeled behaviorvalues comprises calculating the modeled behavior values and their ratesof change over a range of corresponding values of the first processparameter representative of focus.
 11. The method of claim 8, whereincalculating modeled behavior values comprises calculating the modeledbehavior values and their rates of change over a range of correspondingvalues of the first process parameter representative of numericalaperture.
 12. A method, in a computer, for determining an optimumprocess point for fabricating a device feature of a critical dimension,comprising: selecting a measuring point on a computer representation ofa wafer corresponding to the feature of the critical dimension;calculating modeled behavior values and their rates of change over arange of corresponding mask material edge positions; and selecting anoptimum threshold value having the largest rate of change around saidmeasuring point.
 13. The method of claim 12, further comprisingdetermining the mask material edge position corresponding to the optimumthreshold value.
 14. The method of claim 12, wherein calculating modeledbehavior values and their rates of change comprises: selecting a pointon one side of the measuring point; calculating a value of the modeledbehavior at each of the points; and calculating a slope through each ofthe points, wherein the slope is a function of the values of the modeledbehavior at each point.
 15. The method of claim 12, wherein calculatingmodeled behavior values and their rates of change further comprises:shifting the mask material edge position by a first value; calculatingthe value of the modeled behavior at the measuring point; determiningthe value of the modeled behavior at a location offset from themeasuring point in a first direction by a second value; determining thevalue of the modeled behavior at a location offset from the measuringpoint in a second direction, opposite the first direction, by the secondvalue; and calculating the rate of change of the modeled behavior valuecorresponding to the mask material edge position.
 16. The method ofclaim 15, wherein calculating the rate of change comprises: calculatinga difference of the modeled behavior values ascertained duringdetermining the values of the modeled behavior; and dividing thedifference of the modeled behavior values by twice the second value. 17.The method of claim 15, further comprising: providing the optimumthreshold value to a proximity effect correction process which modifiesthe mask material edge position to compensate for proximity effects. 18.A method, in a computer, for determining an optimum process point forfabricating a device feature of a critical dimension, comprising:selecting a measuring point on a computer representation of a wafercorresponding to the feature of the critical dimension; calculatingmodeled behavior values and their rates of change over a range ofcorresponding mask material edge positions, comprising: shifting themask material edge position by a first value; calculating the value ofthe modeled behavior at the measuring point; determining the value ofthe modeled behavior at a location offset from the measuring point in afirst direction by a second value; determining the value of the modeledbehavior at a location offset from the measuring point in a seconddirection, opposite the first direction, by the second value; andcalculating the rate of change of the threshold, comprising: calculatinga difference of the modeled behavior values ascertained duringdetermining the values of the modeled behavior; and dividing thedifference of the modeled behavior values by twice the second value;selecting an optimum threshold value having the largest rate of change;and providing the optimum threshold value to a proximity effectcorrection process which modifies the mask material edge position tocompensate for proximity effects.
 19. A method, in a computer, fordetermining an optimum process point for fabricating a device feature ofcritical dimension, comprising: selecting a plurality of measuringpoints, wherein each measuring point corresponds to the feature of thecritical dimension; calculating values and rates of change of modeledbehavior over a range of values of a first process parameter for eachmeasuring point, the range of values representative of mask materialedge position; selecting an optimum threshold value having the largestrate of change for each measuring point; selecting a threshold valuefrom the plurality of optimum threshold values; and providing theselected threshold value to a proximity effect correction process whichmodifies the mask material edge position to compensate for proximityeffects.
 20. The method according to claim 19, wherein selecting athreshold value includes determining the mean of the selected optimumthreshold values for each measuring point.
 21. The method according toclaim 19, wherein selecting a threshold value includes determining themedian of the selected optimum threshold values for each measuringpoint.
 22. A computer program product comprising a memory havingcomputer program logic recorded thereon for enabling a processor in acomputer system to determine an optimum process point for fabricating adevice feature of a critical dimension, the computer program logiccomprising: a first calculating process enabling the processor tocalculate a modeled behavior value associated with the device featureand a rate of change of the modeled behavior value over a range ofcorresponding values of a first process parameter representative of maskmaterial edge position; a second calculating process enabling theprocessor to select an optimum threshold value having the largest rateof change; and a determining process enabling the processor to determinethe value of the first process parameter corresponding to the optimumthreshold value.
 23. The computer program product of claim 22, furthercomprising: a providing process enabling the processor to provide theoptimum threshold value to a proximity effect correction process whichmodifies the mask pattern to compensate for proximity effects.
 24. Thecomputer program according to claim 22, wherein the first processparameter is a mask material edge position and the rate of change of themodeled behavior value indicates the process latitude in forming thedevice feature associated with a particular mask material edge position.25. A computer system, comprising: a processor; a memory operativelycoupled to the processor; a first calculating process enabling theprocessor to calculate a modeled behavior value associated with thedevice feature and a rate of change of the modeled behavior value over arange of corresponding values of a first process parameterrepresentative of mask material edge positions; a second calculatingprocess enabling the processor to select an optimum threshold valuehaving the largest rate of change; and a determining process enablingthe processor to determine the value of the first process parametercorresponding to the optimum threshold value.
 26. The computer system ofclaim 25, further comprising a providing process enabling the processorto provide the optimum threshold value to a proximity effect correctionprocess which modifies the mask pattern to compensate for proximityeffects.
 27. The computer system of claim 25, wherein the first processparameter is a mask edge position and the rate of change of the modeledvalue indicates the process latitude of an edge of the device feature.